George Osborne is under intense pressure to introduce an immediate overhaul of Britain's banks following a damning assessment by a key member of the new Bank of England body set up to spot risks in the financial system.

In September, the Vickers review called for far-reaching reform of the banking system to prevent a repeat of the 2008 financial crisis but shocked critics when it gave banks until 2019 – much longer than expected – to implement changes to casino-style operations and bonuses.

Jenkins, who spent 16 years running trading floors at major banks, said Osborne should ignore foot-dragging by the banks and lobbyists, and demand that a new deadline of just 24 months be set for implementation of the recommendations in the Vickers report.

After the publication of the Vickers report, Osborne said "detailed work" would start immediately on reforms, promising legislation would be passed in this parliament. But Jenkins said immediate action was vital, noting how US banks were given just one year to comply with the Glass-Steagall act which followed the Great Depression banking collapse.

Jenkins's call comes amid renewed concern about the failure of banks to lend enough cash to support struggling small and medium-sized businesses. Figures from the Bank of England on Monday revealed that the "big five" banks are, on some measures, only lending half the amount to small and medium-sized businesses originally pledged under the Project Merlin deal hammered out between the government and major lenders a year ago.

Last week, the five banks signed up to Project Merlin – Barclays, HSBC, Lloyds Banking Group, RBS and Santander – said they were "on track" to meet targets, loaning £56bn to SMEs in the first nine months, compared with the £76bn full-year target agreed with the government. In the third quarter, the banks lent £18.8bn of the £19bn target.

But Bank of England figures revealed that gross lending to SMEs in the third quarter of 2011 was only £25.5bn, while net lending – after repayments were stripped out – was just £400m.

The Bank of England data is collected on a significantly different statistical basis to Project Merlin, but critics said the figures demonstrate that lending to struggling small businesses is worsening rather than improving.

David Birne, who handles insolvencies at accountants HW Fisher said banks continue to turn their backs on "perfectly viable businesses".

"Rarely has so much self-congratulatory fuss been made over such illusory and pointless targets," he said. "Our experience on the front line is that targets or no targets, simply not enough lending is going on. The banks' lending criteria are frequently so blinkered that they are unable to differentiate the duds from the dynamic. They are not lending nearly enough to keep Britain's embattled SME sector afloat."

Terry Scuoler, chief executive of EEF, the manufacturers' organisation, said he was concerned that the target for SMEs is not being met.

But the Better Business Finance Taskforce, which represents the big five banks, said that most businesses are getting the credit they need to survive. In its last survey of credit conditions, it found that four out of five SMEs had not asked for, or renewed, their lending. Of those that had sought borrowing, 85% were successful in getting an overdraft, and two-thirds of loan applications were approved.

The huge disparity between the figures reported by Merlin and the Bank of England show that the government's lending targets are "meaningless," said Labour shadow Treasury minister Chris Leslie. He said that the Merlin figures are riddled with statistical flaws and also fail to take into account the price businesses have to pay for loans.

The Merlin figures for lending include the value of overdrafts made available to small businesses, even if these overdrafts are not actually used. Crucially, the Bank of England figures focus on lending to the 'real' economy – such as retailers, industry and so on – rather than lending to financial intermediaries and insurers, which is included in the Merlin data.